The government has said the final cost of London's Olympic Games will come in at least £377m under budget and promised the main stadium will not become a white elephant.

Unveiling the government's final quarterly budget update, the sports minister, Hugh Robertson, said that at a "conservative estimate" the final cost of the Games would be £8.921bn against an overall original budget of £9.28bn.

But Olympic organisers conceded that over the course of the project about £1bn of public money had been diverted to the organising committee, Locog, for parts of the project.

Locog, which had a separate, privately raised budget of £2bn to stage the Games, received an additional £16m towards the costs of the Paralympics, £26m towards capital works and £14m for Olympic Park venues and infrastructure during the last quarter.

"The key overriding imperative for government was to make sure that this project worked. By far the most efficient way of doing that was to transfer scope and responsibility to Locog," said Robertson.

"We have done that whenever it seemed the right thing to do and I would do the same again."

The government argues that any funds released to the Locog from the public funding package have been for works that were within originally agreed parameters or were one-off costs such as the extra money diverted to the ceremonies budget.

Robertson said it was "by no means certain" in 2007, when the Labour government announced that the bid budget of £2.4bn had more than tripled to £9.3bn, that the project could be delivered on budget.

He praised the delivery of the Games within the agreed budget, which included more than £2bn of contingency funds, as a "tremendous success" against the backdrop of a global recession.

"The work of the construction and delivery teams, from the ODA [Olympic Delivery Authority] and Locog, has set a very high standard and I have no doubt that London 2012 has set a new benchmark for the management of Olympic and Paralympic Games in future," he said.

Talks are also still ongoing between London 2012 organisers and G4S to get it to pay for the army staff brought in at the last minute.

Robertson said the future of the £429m Olympic Stadium should be concluded "in the next couple of weeks".

Talks are ongoing between the London Legacy Development Corporation (LLDC) and potential tenants, including West Ham.

Negotiations with the club are at an impasse over who will pay for conversion costs of up to £160m to make the stadium suitable for football as well as athletics.

The London mayor, Boris Johnson, is keen to explore the possibility of using some of the unspent contingency, which will flow back to the Treasury, towards the conversion costs.

"Do remember that quite a lot of public money has already gone into the stadium. If the mayor wanted to do it, he will have to have that negotiation with the chancellor," said Robertson.

The LLDC and Johnson have said they would welcome a solution that involved West Ham but "not at any price" and insist that an alternative option to mix concerts with other sports could also pay its way.

"This is a 99-year concession we're talking about so we want to make sure that we get it right. It will take as long as it takes," said the LLDC and ODA chief executive Dennis Hone.

On Tuesday night Great Britain's Olympic and Paralympic heroes were celebrated at a Buckingham Palace reception hosted by the Queen.

The athletes arrived in their official Team GB formal wear of suits, which included a special inside pocket for their medals.

The Queen, joined by the Duke of Edinburgh and the Duchess of Cambridge, had watched the Olympic opening ceremony – and the Queen took part.

Team GB began the summer's medal rush by winning 65 in total, including 29 golds, an achievement that was hailed as the athletes' "greatest ever" performance by Andy Hunt, their chef de mission for London 2012.